Surfaces in 4-manifolds and complex curves

TL;DR

This paper explores the topology of surfaces in 4-manifolds, focusing on complex curves in the complex projective plane, providing insights into their properties and classifications.

Contribution

It offers a topological perspective on complex curves in the projective plane, connecting complex geometry with 4-manifold topology.

Findings

Topological classification of complex curves in CP^2

Insights into surface embeddings in 4-manifolds

Connections between complex geometry and topology

Abstract

These are lecture notes from a mini-course taught at Winterbraids XIII (Montpellier, 2024). The main character of these notes are curves in the complex projective plane, viewed from a topological perspective.